Linear algebra is a special section of algebra that studies linear objects. The linear objects in algebra are:
- vectors and a space of vectors,
- a linear mapping,
- linear equation,
- theory of invariants,
- tensors and operations on tensors,
- etc.
The question may arise, “How does linear algebra relate to programming?” In fact, this is an ingrained question of all aspiring programmers that looks like, “Is there a need for mathematics in programming?” The answer: it all depends on what area of programming you will be working in. For example, if you are going to work in web development, then you will not need a deep knowledge of mathematics, the basic school knowledge will be enough. If you expect to work in the field of artificial intelligence, machine learning or big data, then it will be very difficult for you without mathematics.
By the way, linear algebra is necessary when working on artificial intelligence. There are a lot of mathematical concepts and principles used in this field. Therefore, if you plan to develop in this field as a programmer, then pulling up your knowledge of mathematics is a must. What is linear algebra? We will tell you.
Linear algebra – what is it?
In simple terms, then, linear algebra is a “mathematical activity” formed around a small number of “linear” terms-tools. For example:
- vector,
- scalar,
- tensor,
- matrix.
All of these terms are important when it comes to machine learning and artificial intelligence, so we need to look at each of them in more detail.
Linear algebra: scalar
A scalar is a simple quantity in linear algebra and a regular number. It defines the element of the field in which a vector is described. A vector is formed from a sequence of scalars.
A scalar can be represented by:
- a real number,
- a real number,
- a real number, a natural number.
Linear Algebra: Vector
If you order the scalars in a certain sequence, then you get a vector. Essentially, a scalar in a vector is the coordinates of points in space. If you combine several vectors into a single set, then you get a vector space.
Vectors are amenable to mathematical operations, for example, they can be
add to each other,
multiply them by one another,
and they can be scaled by multiplying each other,
multiply a vector by a number,
etc
To make it easier to work with vectors, each vector has its own index identifier.
Linear Algebra: Matrix
A matrix in linear algebra is a two-dimensional array of scalars. Each individual element in the array has 2 indexes because it is two-dimensional.
When matrices have the same number of columns and rows, then they can be
combine them with each other,
subtract one matrix from another.